Workpieces of large dimensions, typically body pressings or fuselage panels, are supported and secured for machining by a device capable of movement in a vertical direction and adaptable thus to the particular geometry of the workpiece. The vertical movement is produced by a rod of which the top end carries a head incorporating a pivotable fixture mechanism, equipped with a suction cup connected to a source of negative pressure by way of a suction duct and activated to clamp the work once the head is in position.